Tagged Questions

Methods for calculating errors of a function whose arguments have individual errors.

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14 views

Error in standard deviation and variance from error in data

I have a set of datapoints $x_i$ which have known upper bounds for absolute errors $\delta x_i$. (To clarify, this means each $x_i$ is actually $x_{i_0} \pm \delta x_i$). For simplicity, assume that ...
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0answers
18 views

time-series forecasting - predicting av. error intervals

I should start with the disclaimer I'm not proficient with R or heavier statistical terminology, sadly! Nevertheless I create sales forecasts (using different methods such as holt-winters), and I'm ...
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0answers
7 views

Tools for determining final error with mixture of correlated and independent sources of error

Preface: Not looking for an answer, but rather seeking an approach or set of approaches to deal with a complicated problem. Brief version: I have a single, analytical set of 3 equations with 8 ...
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0answers
19 views

How to properly consider uncertainty propagation in random variables

I have 34 input random variables and one output random variable, named R. From 33 input random variables and some dataset I determined the best predictive ...
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0answers
11 views

Error estimation in peak location determination by centroid method

I am trying to locate peak in a data set by numerically calculating the peak using centroid method. How can I estimate the error associated with this peak determination?
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2answers
167 views

Background subtraction for signal and error analysis

I use a CCD to see the split of a energy level due to Zeeman effect. I have a 1 dimensional CCD of 7926 pixel of 7μm each one. My CCD analyze a region 2 dimensional, and then it steps forward 200 ...
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0answers
75 views

Error for combining multiple binomial distributions

This problem is somewhat involved and I have a partial solution so bear with me. I will illustrate the problem with an example. Lets say we have two processes and we want to know which has a higher ...
2
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0answers
46 views

Propagation of Poisson Confidence Intervals

I have a set of measurement with 95% Poisson confidence intervals, and I would like to subtract and multiply them and propagate the error. For example, I measured the copy number of a piece of DNA in ...
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0answers
483 views

Standard deviation of normalized data

I have a data set $y_i$ (where the $y_i$ are photon counts in time period $i$, $i=1,2,...,n$, assumed Poisson), with an estimated standard error $s_i$ (= $\sqrt{y_i}$) for each count. For some ...
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1answer
25 views

Error Propagation Calculation

I have a few machines that are used to calibrate each other. Machine 1 has is accurate to 0.025% Machine 1 is used to calibrate Machine 2, which has an accuracy of 0.005% Machine 2 is used to ...
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0answers
56 views

How do I propagate error when X+Y=1 and aX+bY=1?

I have data for proportions of two diet categories X and Y (from gut samples, n=10) that must sum to 1. I am multiplying each by a different constant (a and b) and then re-calculating the two ...
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2answers
74 views

Statistical error and error propagation

I have a quantity defined as: $P_{frac} = \frac{F_{max}-F_{min}}{F_{max}+F_{min}}$ I also have the value for $F_{max}$, $F_{min}$, and their statistical errors. How can I calculate the error for ...
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0answers
98 views

Error propagation calculation yielding negative variance

I am trying to calculate the standard deviation of the sum X = A + B. A and B are mean values, and I do not have access to the source data. A is 0.46 with an SD of 0.014 (SDa) and B is 0.375 with an ...
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1answer
107 views

How to compare two groups of empirical distributions?

I am working with EEG and now I am trying to compare coherence for two groups of individuals. Problem is coherence is dependent on length of signal but I have signals with different length for each ...
1
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1answer
58 views

Reusing predicted values as independent variables for new linear regression

Edit I've rephrased this question severely. Suppose I have a fitness center, and instead of a monthly fee, the people are paying for courses they are taking. I've got the monthly total revenue of all ...
1
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1answer
152 views

Weighted average of measurements with unequal errors

Suppose I have the numbers below. Consider them as results of some measurement. ...
1
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0answers
43 views

Regression with error in covariates

I am looking for some advice for a colleague who is dealing with regression models for which it is know, that the continuous covariate of interest $X_1$ was measured with error. More precisely, we ...
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1answer
103 views

Possible Paradox: Calculating a confidence interval with within-experiment error

This is a spinoff of How to calculate the confidence interval of the mean of means? and related to When making inferences about group means, are credible Intervals sensitive to within-subject ...
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1answer
361 views

When making inferences about group means, are credible Intervals sensitive to within-subject variance while confidence intervals are not?

This is a spin off of this question: How to compare two groups with multiple measurements for each individual with R? In the answers there (if I understood correctly) I learned that within-subject ...
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3answers
1k views

How to compare two groups with multiple measurements for each individual with R?

I have a problem like the following: 1) There are six measurements for each individual with large within-subject variance 2) There are two groups (Treatment and Control) 3) Each group consists of ...
3
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0answers
210 views

Average over two variables: Why do standard error of mean and error propagation differ and what does that mean?

I'm doing an experiment with a cryostat to determine the critical temperature for lead. To avoid asymmetries, I determine the critical temperature both through heating (going from 2 K to 10 K) and ...
3
votes
1answer
951 views

Multiplication and division of values with geometric standard deviation

What is the geometric standard deviation of a value, which is the result of dividing two independent values, each of which has its own geometric standard deviation ? It is a frequent situation in ...
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0answers
233 views

Division of two poisson variables

Let's say I have four variables $x_1, x_2, x_3$ and $x_4$ all distributed as Poisson, with means $\lambda_i$, and standard deviations respectively. Now I want to calculate two further variables $y_1= ...
5
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1answer
117 views

Error of the sum of complex numbers

I'm analyzing the effect of precision error in optics experiments. One of the relevant quantities is a sum of $N$ complex numbers, each with a complex relative standard error $\epsilon$. How can I ...
0
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1answer
147 views

Formal errors from non-negative least-squares?

I have seen a couple of similar questions, but none with answers, so perhaps I can formulate this question in a way that will be answerable. I am computing a standard linear regression subject to a ...
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votes
2answers
166 views

Error propagation SD vs SE

I have 3 to 5 measures of a trait per individual in two different conditions (A and B). I'm plotting the average for each individual in each condition and I use the standard error (i.e., ...
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0answers
34 views

Explaining the difference between error propagation and “grand variance”?

I have the following data concerned with simple radiation detection. I collect a background dose $B$ for 100 seconds and find the standard deviation and get the uncertainty $E_B$. I then take 10 ...
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2answers
88 views

Calculate effect of independent variable

If $a\times b\times c=t$ and I change $a$, $b$, and $c$, how do I calculate the effect of each change. I believe the equation is: $(a+\Delta a)(b+\Delta b)(c+\Delta c)=(t+\Delta t)$, and then I solve ...
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0answers
46 views

Combining errors

I've got this tricky problem to solve. Hope somebody can help me. Let's suppose I want to know the mean radius of the trees in a wood. For each tree i I measure the radius at the top, at tha center ...
0
votes
1answer
167 views

Simulating Monte Carlo with different standard deviations and interval confidence

I have a question regarding Monte Carlo simulation (direct simulation), applied to propagation of uncertainties. From what I understand Monte Carlo accepts random numbers of each input variable of ...
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0answers
38 views

posterior covariance for linear inversion

I am performing a physical experiment where the unavoidably inaccurate setup likely creates errors in the inversion of the data for the model. Let's assume a linear relationship between data $\mathbf ...
5
votes
0answers
408 views

Uncertainty propagation in linear interpolation

How do I calculate the uncertainties in linearly interpolated values from a given tabulated function? I am just coming back into the fold after a bit of a hiatus, and am having trouble ...
0
votes
1answer
39 views

Combining observed Gaussian error with common fractional model error

I'm currently trying to incorporate model errors into a likelihood function to fit the model to some results. Let's just call them $x_{m,i}$ for the model and $x_{o,i}$ for the $N$ observations, ...
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1answer
104 views

How do I calculate the error propagation of this function?

I'm using a molecular biological method which requires the following normalization $$Q = \frac{A}{\sqrt[k]{\prod_{i=1}^k B_i}}.$$ How can I find the standard deviation of $Q$, given that $A$ and ...
3
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0answers
307 views

Error propagation with linear regression

I'm trying to obtain an estimation of the uncertainty related to an analytical method: my function is just a linear regression $f: y=ax+b+ \epsilon$ with $y_i=\frac{R_i}{C}$, both $R$ and $C$ are ...
0
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0answers
766 views

Standard error of fold changes

I have a conceptual problem to understand the standard error of the ratio of two random variables after error propagation. Let $X$ and $Y$ be two random variables with means $\bar x$ and $\bar y$ and ...
2
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0answers
54 views

Variance in a known population

I am working on a problem that is similar to the standard radioactive decay rate experiment, but with a twist. In the normal experiment, one takes several different measurements of the decay rate, ...
0
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0answers
81 views

Error bars on a logarithm

I'm plotting the following point using python (a and b have are non gaussian): x=np.log10(a) y=np.log10(b) xmedian=np.median(x) ymedian=np.median(y) and I ...
2
votes
1answer
473 views

Propagation of uncertainty through a linear system of equations

If I have a system of equations, $Ax=B$ where the elements of $B$ have been experimentally determined and as such each element has some uncertainty, how would I propagate this to the elements of $x$? ...
0
votes
1answer
308 views

Mean of means -> error propagation or uncertainty or both?

my problem is as follows. I have a simulation of a neural network which creates activity patterns, learns them and then tries to retrieve previously learned patterns one by one. The performance of ...
0
votes
1answer
207 views

Propagation of errors with median absolute deviation from the median?

Is there a theoretically-sound way to perform propagation of errors with robust statistics? I am trying to characterize the errors inherent in a measurement and propagate the uncertainty through ...
1
vote
2answers
92 views

Propagation of errors using simulation

If I construct confidence intervals for a calculation based on simulating inputs rather than using error propagation formulas, would this be considered as belonging to 'Monte Carlo' methods? I would ...
1
vote
1answer
70 views

statistical error on difference f(x) - x

Suppose I've a random variable $X$ and a sample of it with size $N$. I count how many element of the sample fall in a specific range $a<x<b$ and I found $n$ entries, so if I use Poisson ...
1
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1answer
253 views

Propagation of uncertainty through an average

I have a set of distance measurements that are all accurate to +/- 0.01 M. {1.00,2.00,3,00} We can obtain the distance moved ...
2
votes
1answer
366 views

Uncertainty on parameter of unknown function

I have a collection of data points, which are counts as a function of length. Each data point is the result of many trials and has an error bar. The function ...
3
votes
1answer
366 views

Median Averaging and Error Analysis

I am not sure if i should be asking this on the Mathematics of Physics Stack Exchange site. I am taking data for a physics research application and have a question about using median vs. mean ...
1
vote
1answer
82 views

Error propagation and under-represented variable

I am running a relatively simple propagation of error analysis on an equation: $$S = \frac{ABC}{XY}$$ I have independent random error terms calculated for each variable (for the purposes of this ...
1
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0answers
80 views

Error estimation and propagation

Suppose I pull from literature a relationship between $X$ and $Y$ with reported confidence intervals from a linear regression $$Y = 2\ (\pm .5) + 5\ (\pm .2)X$$ and then another relationship between ...
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0answers
50 views

Error of generalized classifier performance

I am working on a problem where it is expensive to label data and I have sampled a small subset of the available data and labeled it. My classifier is a binary classifier that I use with the hope of ...
2
votes
1answer
99 views

Systematic vs. statistical error

I'm currently working with some measurements of the following form: Three test subjects, three trials per test subject, three measurement points per trial: At each measurement point within each ...